Application of total light reflection. The phenomenon of total internal reflection of light and its application

The propagation of electromagnetic waves in various media obeys the laws of reflection and refraction. From these laws, under certain conditions, one interesting effect follows, which in physics is called the total internal reflection of light. Let's take a closer look at what this effect is.

Reflection and refraction

Before proceeding directly to the consideration of the internal total reflection of light, it is necessary to give an explanation of the processes of reflection and refraction.

Reflection is understood as a change in the direction of movement of a light beam in the same medium when it encounters an interface. For example, if you direct from a laser pointer to a mirror, you can observe the described effect.

Refraction is, like reflection, a change in the direction of light movement, but not in the first, but in the second medium. The result of this phenomenon will be a distortion of the outlines of objects and their spatial arrangement. A common example of refraction is the breaking of a pencil or pen if he/she is placed in a glass of water.

Refraction and reflection are related to each other. They are almost always present together: part of the energy of the beam is reflected, and the other part is refracted.

Both phenomena are the result of the application of Fermat's principle. He claims that light travels along a trajectory between two points that will take him the least time.

Since reflection is an effect that occurs in one medium, and refraction occurs in two media, it is important for the latter that both media are transparent to electromagnetic waves.

The concept of refractive index

The refractive index is an important quantity for the mathematical description of the phenomena under consideration. The refractive index of a particular medium is determined as follows:

Where c and v are the speeds of light in vacuum and matter, respectively. The value of v is always less than c, so the exponent n will be greater than one. The dimensionless coefficient n shows how much light in a substance (medium) will lag behind light in a vacuum. The difference between these speeds leads to the appearance of the phenomenon of refraction.

The speed of light in matter correlates with the density of the latter. The denser the medium, the harder it is for light to move in it. For example, for air n = 1.00029, that is, almost like for vacuum, for water n = 1.333.

Reflections, refraction and their laws

A striking example of the result of total reflection are the shiny surfaces of a diamond. The refractive index for a diamond is 2.43, so many light rays hitting a gem experience multiple total reflections before leaving it.

The problem of determining the critical angle θc for diamond

Let's consider a simple problem, where we will show how to use the above formulas. It is necessary to calculate how much the critical angle of total reflection will change if a diamond is placed from air into water.

Having looked in the table for the values ​​for the refractive indices of the indicated media, we write them out:

• for air: n 1 = 1.00029;
• for water: n 2 = 1.333;
• for diamond: n 3 = 2.43.

The critical angle for a diamond-air pair is:

θ c1 \u003d arcsin (n 1 / n 3) \u003d arcsin (1.00029 / 2.43) ≈ 24.31 o.

As you can see, the critical angle for this pair of media is quite small, that is, only those rays can leave the diamond into the air that will be closer to the normal than 24.31 o .

For the case of a diamond in water, we get:

θ c2 \u003d arcsin (n 2 / n 3) \u003d arcsin (1.333 / 2.43) ≈ 33.27 o.

The increase in the critical angle was:

Δθ c \u003d θ c2 - θ c1 ≈ 33.27 o - 24.31 o \u003d 8.96 o.

This slight increase in the critical angle for the total reflection of light in diamond leads to the fact that it glistens in water almost the same as in air.

Typical lighting effects that every person often encounters in everyday life are reflection and refraction. In this article, we will consider the case when both effects manifest themselves within the same process, we will talk about the phenomenon of internal total reflection.

reflection of light

Before considering the phenomenon, one should get acquainted with the effects of ordinary reflection and refraction. Let's start with the first one. For simplicity, we will consider only light, although these phenomena are characteristic of a wave of any nature.

Reflection is understood as a change from one rectilinear trajectory, along which a ray of light moves, to another rectilinear trajectory, when it encounters an obstacle in its path. This effect can be observed when pointing a laser pointer at a mirror. The appearance of images of the sky and trees when looking at the water surface is also the result of the reflection of sunlight.

The following law is valid for reflection: the angles of incidence and reflection lie in the same plane together with the perpendicular to the reflecting surface and are equal to each other.

Light refraction

The effect of refraction is similar to reflection, only it occurs if the obstacle in the path of the light beam is another transparent medium. In this case, part of the initial beam is reflected from the surface, and part passes into the second medium. This last part is called the refracted beam, and the angle it makes with the perpendicular to the interface is called the angle of refraction. The refracted beam lies in the same plane as the reflected and incident beams.

Vivid examples of refraction include the break of a pencil in a glass of water or the deceptive depth of a lake when a person looks down on its bottom.

Mathematically, this phenomenon is described using Snell's law. The corresponding formula looks like this:

Here, the refractions are denoted as θ 1 and θ 2, respectively. The values ​​n 1 , n 2 reflect the speed of light in each medium. They are called the refractive indices of the media. The larger n, the slower the light travels in a given material. For example, the speed of light in water is 25% less than in air, so for it the refractive index is 1.33 (for air it is 1).

The phenomenon of total internal reflection

Leads to one interesting result when the ray propagates from a medium with large n. Let us consider in more detail what will happen to the beam in this case. We write out the Snell formula:

n 1 * sin (θ 1) \u003d n 2 * sin (θ 2).

We will assume that n 1 >n 2 . In such a case, for the equality to remain true, θ 1 must be less than θ 2 . This conclusion is always valid, since only angles from 0 o to 90 o are considered, within which the sine function is constantly increasing. Thus, when leaving a denser optical medium for a less dense one (n 1 >n 2), the beam deviates more from the normal.

Now we will increase the angle θ 1 . As a result, the moment will come when θ 2 will be equal to 90 o . An amazing phenomenon arises: a beam emitted from a denser medium will remain in it, that is, for it the interface between two transparent materials will become opaque.

Critical angle

The angle θ 1 for which θ 2 = 90 o is usually called critical for the considered pair of media. Any ray that strikes the interface at an angle greater than the critical angle is reflected completely into the first medium. For the critical angle θ c, one can write an expression that follows directly from the Snell formula:

sin (θ c) \u003d n 2 / n 1.

If the second medium is air, then this equality is simplified to the form:

sin (θ c) \u003d 1 / n 1.

For example, the critical angle for water is:

θ c \u003d arcsin (1 / 1.33) \u003d 48.75 o.

If you dive to the bottom of the pool and look up, you can see the sky and clouds running across it only above your own head, on the rest of the water surface only the walls of the pool will be visible.

It is clear from the above reasoning that, unlike refraction, total reflection is not a reversible phenomenon; it occurs only during the transition from a denser to a less dense medium, but not vice versa.

Full reflection in nature and technology

Perhaps the most common effect in nature, which is impossible without total reflection, is the rainbow. The colors of the rainbow are the result of the dispersion of white light in raindrops. However, when the rays pass inside these droplets, they experience either single or double internal reflection. That is why the rainbow always appears double.

The phenomenon of internal total reflection is used in fiber optic technology. Thanks to optical fibers, it is possible to transmit electromagnetic waves without loss over long distances.

2. Reflection and refraction of light. total internal reflection. Fiber optics, its application in medicine.

From the theory of the electromagnetic field developed by J. Maxwell, it followed: electromagnetic waves propagate at the speed of light - 300,000 km / s, that these waves are transverse, just like light waves. Maxwell suggested that light is an electromagnetic wave. Later, this prediction was experimentally confirmed.

Like electromagnetic waves, the propagation of light obeys the same laws.

The law of reflection. The angle of incidence is equal to the angle of reflection (α=β). The incident ray AO, the reflected ray OB, and the perpendicular OS raised at the point of incidence lie in the same plane.

The law of refraction. The incident beam AO and the refracted OF lie in the same plane with the perpendicular CD drawn at the point of incidence of the beam to the plane of separation of the two media. The ratio of the sines of the angle of incidence a and the angle of refraction y is constant for these two media and is called the refractive index of the second medium with respect to the first: .

The laws of light reflection are taken into account when constructing an image of an object in mirrors (flat, concave and convex) and appear in mirror reflection in periscopes, searchlights, car headlights and in many other technical devices. The laws of light refraction are taken into account when constructing an image in various lenses, prisms and their combination (microscope, telescope), as well as in optical instruments (binoculars, spectral devices, cameras and projection devices). If a light beam follows from an optically less dense medium (for example, from air; n air = 1) to an optically denser medium (for example, into glass with a refractive index n st. = 1.5), then partial reflection and partial light refraction.

It follows that , that is, the sine of the angle of refraction g is less than the sine of the angle of incidence a, by 1.5 times. And if sing

If, on the other hand, a light beam is launched from optically denser glass into optically less dense air, then the angle of refraction will, on the contrary, be greater than the angle of incidence, g > a. For the considered retrace of the beam, the law of refraction is:

hence sing = 1.5sina; g>a

This situation is illustrated by diagram A in Figure

If the angle of incidence a is increased to a certain limiting value a pr, then the angle of refraction g > a reaches its maximum value g=90 0 . The refracted beam slides along the interface between two media. At angles of incidence a > a, refraction does not occur, and instead of partial reflection at the phase boundary, complete reflection of light into an optically denser medium, or total internal reflection . This optical phenomenon forms the basis of a whole physical and technical direction, which is called fiber optics.

In medicine, fiber optics has found application in endoscopes - devices for examining internal cavities (for example, the stomach). The light guide, which is a bundle of a large number of thin glass fibers placed in a common protective sheath, is inserted into the cavity under study. Part of the fibers is used to organize the illumination of the cavity from a light source located outside the patient's body. The light guide can also be used to transmit laser radiation into the internal cavity for medical purposes.

Total internal reflection also occurs in some structures of the retina.

3. Optical system of the eye. Visual defects, methods of their correction .

The optical system of the eye provides a reduced real reverse (inverted) image on the retina. If the refractive system of the eye is considered as one lens, then the total optical power of this system is obtained as the algebraic sum of the following four terms:

a) Cornea: D = +42.5 diopters

b) Front camera: D from +2 to +4 diopters

c) Lens: D  const; from +19 to +33 diopters

d) Vitreous body; D from -5 to -6 diopters.

Due to the fact that the optical power of the lens is a variable value, the total optical power of the eye lies in the range from 49 to 73 diopters.

The reduced eye, like a single lens, faces the air on one side (absolute refractive index nair = 1), and the other is in contact with the liquid, nl=1.336. So the left and right focal lengths are not the same; if the front focal length is on average F1 = 17 mm, then the rear focal length is F2 = 23 mm. The optical center of the system is in the depth of the eye at a distance of 7.5 mm from the outer surface of the cornea.

The main refractive element of this system - the cornea - has not a spherical, but a more complex shape of refractive surfaces, and this is a good blow to spherical aberration.

The lens changes its optical power with contraction or relaxation of the cirial muscles; this achieves accommodation of the eye - its adaptation to focusing the image on the retina both when viewing distant and close objects. The necessary tension of these muscles gives information about the distance to the object in question, even if we consider it with one eye. The total amount of light entering the eye is regulated by the iris. It can be different in color, and therefore people are blue-eyed, brown-eyed, etc. It is controlled by a pair of muscles. There is a muscle that constricts the pupils (circular muscle), there is a muscle that expands it (radial muscle).

Consider further the structural features of the retina. Its purpose is to convert the optical image obtained on its surface into streams of electrical nerve impulses entering the brain. These transformations are carried out by photoreceptor cells of two types, which, due to the peculiarities of their shape, have received the name cones and rods.

Cones are photoreceptors for daytime vision. Provide color vision. Rods are receptors for twilight vision. Each human eye contains approximately 125*106 rods and 5*106 cones, for a total of 130*106 photoreceptors. Cones and rods are very unevenly distributed over the retina: only rods are located on the periphery, the closer to the area of ​​the macula, the more cones are found; only cones are located in the macula, and their density (the number per unit area) is very high, so here these cells are even “manufactured” in a small-sized version - they are smaller than in other areas of the retina.

The area of ​​the macula of the retina is the area of ​​the best vision. Here we focus the image of the subject, if we want to see this subject especially carefully.

The density of the "packing" of cones in the macula determines the sharpness of our vision. This density, on average, is such that three cones fit on a segment 5 microns long. In order for the eye to distinguish between two points of an object, it is necessary that between two illuminated cones there must be one not illuminated one.

Refraction (refraction) of light in the eye is normal if the image of the object given by the optical system of the eye lies on the outer segments of the photoreceptors, and at the same time the muscles that control the curvature of the lens are relaxed. This (normal) refraction is called emmetropia.

Deviation from emmetropia - ametropia - occurs in two varieties. Myopia (myopia) - the image is not focused on the retina, but in front of it, that is, the refraction of light in the eye is "too good". This redundancy can be eliminated by diverging spectacle lenses (optical power is negative).

Hypermetropia (farsightedness) - a type of ametropia, in which the image is formed behind the retina. To return the image to the retina, it is necessary to "help" the eye with a converging spectacle lens (optical power is positive). In other words, if the optical power of the eye is insufficient, it can be increased by an additional term - the optical power of the converging spectacle lens.

The appearance of contact lenses instead of classic glasses was at first perceived almost as a revolution.

When discussing the possibilities of a contact lens, it must be taken into account that the relative refractive index on the first (along the beam) surface of the contact lens is actually equal to the absolute refractive index of the lens material, and on the second surface it is equal to the ratio of the absolute refractive indices of the cornea and lens.

When implementing any invention, sooner or later, both advantages and disadvantages are discovered. Classic glasses and contact lenses, in their current form, can be compared as follows:

Classic glasses are easy to put on and take off, but not comfortable to wear;

Contact lenses are comfortable to wear, but not easy to put on and take off.

Laser vision correction is a micro-surgery on the outer surface of the cornea. Recall that the cornea is the main light-refracting element of the optical system of the eye. Vision correction is achieved by changing the curvature of the outer surface of the cornea. For example, if the surface is made flatter (i.e., the radius of curvature R is increased), then, according to formula (4), the optical power D of this surface will decrease.

Serious vision problems occur when the retina is detached. In these cases, the method of fixing the retina in the place provided by nature with the help of a focused laser beam has found application. This fixing method is similar to spot welding of metals in engineering. A focused beam creates a small zone of elevated temperature, in which the "welding" of biological tissues takes place (literally and figuratively).

Retinal - one of the two main components of rhodopsin - is vitamin A aldehyde. Taking into account the fact that the outer segments of photoreceptors are constantly updated, a full supply of vitamin A to the body is in the interests of maintaining the visual system in good condition.

4 . Optical microscope. The path of rays in a microscope. Useful magnification of a microscope.

Microscope - a device designed to obtain enlarged images, as well as to measure objects or structural details that are invisible or poorly visible to the naked eye. It is a collection of lenses.

The combination of manufacturing technologies and practical use of microscopes is called microscopy. In a microscope, mechanical and optical parts are distinguished. The mechanical part is represented by a tripod (consisting of a base and a tube holder) and a tube mounted on it with a revolver for mounting and changing lenses. The mechanical part also includes: an object table for the preparation, devices for fixing the condenser and light filters, mechanisms built into the tripod for coarse (macromechanism, macroscrew) and fine (micromechanism, microscrew) movement of the object table or tube holder.

The optical part is represented by lenses, eyepieces and an illumination system, which in turn consists of an Abbe condenser located under the object stage and a built-in illuminator with a low-voltage incandescent lamp and a transformer. The objectives are screwed into the revolver, and the corresponding eyepiece, through which the image is observed, is installed on the opposite side of the tube.

The mechanical part includes a tripod consisting of a base and a tube holder. The base serves as a support for the microscope and carries the entire tripod structure. There is also a socket for a mirror or a built-in illuminator at the base of the microscope.

the subject little table serving for placement of preparations and their horizontal movement;

node for mounting and vertical light filters.

Useful magnification - this is the apparent magnification at which the observer's eye will fully use the resolution of the microscope, that is, the resolution of the microscope will be the same as the resolution of the eye. formula

where d1 is the maximum resolution of the human eye, equal to 0.3 mm; d is the maximum resolution of the optical system.

(Fiber optics) Practical application of the phenomenon of total reflection!

Application of total reflection of light 1. When a rainbow is formed 2. To direct light along a curved path

Scheme of rainbow formation 1) spherical drop, 2) internal reflection, 3) primary rainbow, 4) refraction, 5) secondary rainbow, 6) incoming light beam, 7) ray path during the formation of the primary rainbow, 8) ray path during the formation of the secondary rainbow , 9) observer, 10-12) region of rainbow formation.

To direct light along a curved path, optical fibers are used, which are thin (from several micrometers to millimeters) arbitrarily curved filaments made of optically transparent material (glass, quartz). Light falling on the end of the fiber can propagate along it over long distances due to total internal reflection from the side surfaces. Optical fibers are used to make cables for fiber-optic communication. Fiber-optic communication is used for telephone communications and high-speed Internet

Optical fiber cable

Optical fiber cable

Advantages of FOCL Fiber-optic lines have a number of advantages over wired (copper) and radio relay communication systems: Low signal attenuation allows information to be transmitted over a much longer distance without the use of amplifiers. The high bandwidth of optical fiber makes it possible to transmit information at a high speed, unattainable for other communication systems. High reliability of the optical environment: optical fibers do not oxidize, do not get wet, and are not subject to weak electromagnetic effects. Information security - information is transmitted via optical fiber "from point to point". It is impossible to connect to the fiber and read the transmitted information without damaging it. High protection against interfiber influences. Radiation in one fiber does not affect the signal in the neighboring fiber at all. Fire and explosion safety when measuring physical and chemical parameters Small dimensions and weight Disadvantages of FOCL Relative fragility of the optical fiber. With a strong bending of the cable, the fibers may break or become cloudy due to the occurrence of microcracks. Sophisticated manufacturing technology of both the fiber itself and the FOCL components. Difficulty in signal conversion Relative cost of optical termination equipment Fiber clouding over time due to aging.

Optical fiber illumination

Endoscope (from Greek ένδον - inside and Greek σκοπέω - inspection) - a group of optical instruments for various purposes. There are medical and technical endoscopes. Technical endoscopes are used to inspect hard-to-reach cavities of machines and equipment during maintenance and performance assessment (turbine blades, internal combustion engine cylinders, pipeline condition assessment, etc.), in addition, technical endoscopes are used in security systems to inspect hidden cavities (in including for inspection of gas tanks at customs Medical endoscopes are used in medicine to examine and treat hollow internal organs of a person (esophagus, stomach, bronchi, urethra, bladder, female reproductive organs, kidneys, hearing organs), as well as abdominal and other body cavities .

Thank you for your attention!)

Some laws of physics are difficult to imagine without the use of visual aids. This does not apply to the usual light falling on various objects. So, at the boundary separating two media, a change in the direction of light rays occurs if this boundary is much greater than when light occurs when part of its energy returns to the first medium. If part of the rays penetrates into another medium, then they are refracted. In physics, energy that hits the boundary of two different media is called incident, and the one that returns from it to the first medium is called reflected. It is the mutual arrangement of these rays that determines the laws of reflection and refraction of light.

Terms

The angle between the incident beam and the line perpendicular to the interface between two media, restored to the point of incidence of the light energy flux, is called There is another important indicator. This is the angle of reflection. It occurs between the reflected beam and the perpendicular line restored to the point of its incidence. Light can propagate in a straight line only in a homogeneous medium. Different media absorb and reflect light radiation in different ways. The reflection coefficient is a value that characterizes the reflectivity of a substance. It shows how much energy brought by light radiation to the surface of the medium will be that which is carried away from it by reflected radiation. This coefficient depends on a number of factors, one of the most important being the angle of incidence and the composition of the radiation. Total reflection of light occurs when it falls on objects or substances with a reflective surface. So, for example, this happens when rays hit a thin film of silver and liquid mercury deposited on glass. Total reflection of light is quite common in practice.

Laws

The laws of reflection and refraction of light were formulated by Euclid as early as the 3rd century. BC e. All of them have been established experimentally and are easily confirmed by the purely geometric principle of Huygens. According to him, any point of the medium, to which the perturbation reaches, is a source of secondary waves.

First light: the incident and reflecting beams, as well as the perpendicular line to the interface, restored at the point of incidence of the light beam, are located in the same plane. A plane wave is incident on a reflective surface, the wave surfaces of which are stripes.

Another law states that the angle of reflection of light is equal to the angle of incidence. This is because they have mutually perpendicular sides. Based on the principles of equality of triangles, it follows that the angle of incidence is equal to the angle of reflection. It can be easily proved that they lie in the same plane with the perpendicular line restored to the interface between the media at the point of incidence of the beam. These most important laws are also valid for the reverse course of light. Due to the reversibility of energy, a beam propagating along the path of the reflected will be reflected along the path of the incident.

Properties of reflective bodies

The vast majority of objects only reflect the light radiation incident on them. However, they are not a source of light. Well-lit bodies are perfectly visible from all sides, since the radiation from their surface is reflected and scattered in different directions. This phenomenon is called diffuse (scattered) reflection. It occurs when light hits any rough surface. To determine the path of the beam reflected from the body at the point of its incidence, a plane is drawn that touches the surface. Then, in relation to it, the angles of incidence of rays and reflection are built.

diffuse reflection

Only due to the existence of diffuse (diffuse) reflection of light energy do we distinguish between objects that are not capable of emitting light. Any body will be absolutely invisible to us if the scattering of rays is zero.

Diffuse reflection of light energy does not cause discomfort in the eyes of a person. This is due to the fact that not all light returns to its original environment. So about 85% of the radiation is reflected from snow, 75% from white paper, and only 0.5% from black velor. When light is reflected from various rough surfaces, the rays are directed randomly with respect to each other. Depending on the extent to which surfaces reflect light rays, they are called matte or mirror. However, these terms are relative. The same surfaces can be specular and matte at different wavelengths of incident light. A surface that scatters rays evenly in different directions is considered absolutely matte. Although there are practically no such objects in nature, unglazed porcelain, snow, and drawing paper are very close to them.

Mirror reflection

Specular reflection of light rays differs from other types in that when beams of energy fall on a smooth surface at a certain angle, they are reflected in one direction. This phenomenon is familiar to anyone who has ever used a mirror under the rays of light. In this case, it is a reflective surface. Other bodies also belong to this category. All optically smooth objects can be classified as mirror (reflective) surfaces if the sizes of inhomogeneities and irregularities on them are less than 1 micron (do not exceed the wavelength of light). For all such surfaces, the laws of light reflection are valid.

Reflection of light from different mirror surfaces

In technology, mirrors with a curved reflective surface (spherical mirrors) are often used. Such objects are bodies having the shape of a spherical segment. The parallelism of the rays in the case of reflection of light from such surfaces is strongly violated. There are two types of such mirrors:

Concave - reflect light from the inner surface of a segment of the sphere, they are called collecting, since parallel rays of light after reflection from them are collected at one point;

Convex - reflect light from the outer surface, while parallel rays are scattered to the sides, which is why convex mirrors are called scattering.

Options for reflecting light rays

A beam incident almost parallel to the surface only slightly touches it, and then is reflected at a very obtuse angle. It then continues on a very low trajectory, as close to the surface as possible. A beam falling almost vertically is reflected at an acute angle. In this case, the direction of the already reflected beam will be close to the path of the incident beam, which is fully consistent with physical laws.

Light refraction

Reflection is closely related to other phenomena of geometric optics, such as refraction and total internal reflection. Often, light passes through the boundary between two media. Refraction of light is a change in the direction of optical radiation. It occurs when it passes from one medium to another. The refraction of light has two patterns:

The beam that passed through the boundary between the media is located in a plane that passes through the perpendicular to the surface and the incident beam;

The angle of incidence and refraction are related.

Refraction is always accompanied by reflection of light. The sum of the energies of the reflected and refracted beams of rays is equal to the energy of the incident beam. Their relative intensity depends on the incident beam and the angle of incidence. The structure of many optical devices is based on the laws of light refraction.